If you can't see that distinction from how I wrote it above, then we are going to have to agree to disagree because I think it's pretty clear from where I stand.
>>asking people to counter Moore's voice.
Then say Protest the movie, hand out oposing literature, finance a movie with an opposing POV.
You're asking businesses to stop showing it. You're calling for the abrogation of that business's privilege to show what they want, and infringing upon the freedom of those who wish to see the movie.
I still don't understand the difference between Ban and Stop. The end result is the same; you want the movie pulled. If you don't, then using the word stop is misleading.
I think you're splitting hairs semantically, and that kind of tap dancing is not convincing.